Interest: The
money paid by the borrower to the lender for the use of money is called
Interest.
Principal: The
sum lent is called the principal.
Simple
Interest =
PTR
100
Where
P = Principal R= Rate of interest per annum
T=
Time period in years
Amount=
Principal + Simple Interest
Amount=>
A = P x $\frac{100+RT}{2}$
Solved
Problems on Simple Interest:
1.
Find the simple interest on
Rs 8000 for 5 years at 10% p.a rate of interest?
a)
Rs 3500 b)Rs 4000 c)Rs 2400 d)Rs
4800
Answer : B
Explanation : Simple Interest =
PTR
100
= 8000 X 5 X
10
100
= Rs 4000
2.
Find the simple interest on
Rs 2400 for 8 years 4 months at 6% per annum rate of interest ?
a)Rs 750 b)Rs
800 c)Rs 600 d)Rs 1200
Answer : D
Explanation:
Time period is 8 years 4 months = 8
4
12
years =
25
3
years
Simple Interest =
PTR
100
= 2400 x
25
3
x
6
100
=Rs
1200
3. What is the simple interest
on Rs 8000 from August 6th to December 30th at 5% p.a
rate of interest?
a)Rs 240 b)Rs
200 c)Rs 160 d)Rs 120
Answer: C
Explanation:
Number of days from August 6th to December 30th = 146
days ( we don’t count the given day)
Simple
Interest=
PTR
100
= 8000 x
146
365
x
5
100
= Rs 160
4.
What is the simple interest
on Rs 2400 for 9 months at 4 paisa per
rupee per month?
a)Rs 864 B)Rs
800 c)Rs 432 d)Rs 216
Answer: A
Explanation: P
= Rs 2400 Time Period T = 9 months =
9
12
years = ¾ year
Rate of
interest =4 paisa per Rupee per month= 4% per month= 48% p.a
Simple Interest=
PTR
100
= 2400 X $\frac{3}{4}$
X
48
100
= Rs 864
5.
At what rate of interest per
annum, will Rs 5500 be obtained as simple interest on Rs 25000 for 2 years 9
months?
a)
10% b)9% c)8% d)7%
Answer :
Explanation:
Given P= Rs 25000 and
Time period = 2 years 9 months= 2
9
12
=
11
4
years
Simple
Interest=
PTR
100
5500 = 25000 X
11
4
X
R
100
R = 8 %
6.
A man borrowed Rs 10000 from a lender at 9% per annum rate of
interest .Find the amount to be paid by the man after 2 years 6 months?
a)
Rs 12000 b)Rs 12500 c)Rs 12250 d)Rs 15000
Answer :C
Explanation:
Principal
= Rs 10000 Rate of interest R =
9%
T=
2 years 6 months= 2 ½ years=
5
2
years
Simple
Interest=
PTR
100
= 10000 X
5
2
X
9
100
= Rs 2250
Amount= Prinipal + Simple interest = Rs
10000+ Rs 2250 = Rs 12250
Alternate
Method:
We have a direct formula to find the amount
A= P
(100+RT)
100
= 10000 $ \frac{100+\frac{5}{2}\times9}{100}$
= Rs 12250
7.
Sharma deposited Rs 9000 in a
financial institution at 8% per annum rate of interest for 3 years. For many
years must Tripathi deposit Rs 5,400 at 10% per annum rate of interest in
another financial institution so that both of them get the same simple interest?
a)
4 years b)10 years c)12 years d)9 years
Answer: A
Explanation:
The simple interest on Rs 9000 at 8% rate of interest for 3 years should be equal
to the simple interest on Rs 5400 at 10% for unknown years.
9000 X 3 X
8
100
= 5400 X T
x
10
100
Therefore T = 4 years
Tripathi
should deposit for 4 years to get the same interest as Sharma
8.
Mr. Bhattacharyya lent Rs 3600
to Mr. Tiwary for 3 years and Rs 6600 to Mr.Mishra for 2 years , and he received
Rs 1200 as a simple interest in all. Find
the rate of interest per annum?
a)
4% b)5% c)6% d)12%
Answer:
B
Explanation:
(SI on 3600 for 3 years + SI on Rs 6600 for 2 years) = 1200
(3600 x 3 x
R
100
) +( 6600 x 2 x
R
100
) = 1200
ð 108R
+132R = 1200
ð 240R=
1200
ð R=
5%
The
rate of interest per annum is 5%
9.
The simple interest on a sum
of money is $ \frac{1}{25}$
th of the principal. If the rate of interest is 16%. Find the
time period?
a)
1 month b)2 months c)3 months d)4 months
Answer: C
Explanation:
Simple interest is
1
25
of the principal => SI =
1
25
P
1
25
P= P
x
16
100
x T=>T= $\frac{1}{4}$
years
Therefore, the time period is
1
4
th year = 3
months
10. The simple interest on a sum of money is $\frac{4}{25}$
of the principal
and the rate of interest is equal to the number of years . What is the rate of
interest?
a)4% b)8% c)16% d)18%
Answer : A
Explanation :
Simple interest is
Rate of interest per annum is equal to the number of years => R =T
Simple interest is
4
25
th of the principal => SI =
4
25
P.Rate of interest per annum is equal to the number of years => R =T
SI =
PTR
100
4
25
P = P X R X
R
100
=>R2 =
400
25
=>R=
20
5
=4%
11. A sum was put at simple
interest at a certain rate of 4 years. Had it been put a 3% higher rate, it
would have fetched Rs 720 more. Find the principal?
a)Rs 4500 b)Rs 5000 c)Rs 6000 d)Rs
7200
Answer:C
Explanation: Let the rate of interest be R and principal be P.
SI at R rate of interest=> SI = P X 4 x
If the rate of interest is 4% more, then SI= P X 4 x
R
100
If the rate of interest is 4% more, then SI= P X 4 x
(R+3)
100
The difference between these two simple interests is Rs
720
P X 4 x
(R+3)
100
- P X 4 x
R
100
= 720
P X
4 X
3
100
= 720
Therefore P= Rs 6000
12. Mr. Shastri invested a certain sum of money at 7% p.a for 4 years.
However, he would get Rs 1040 more simple interest if he invests the same sum
of money at 6% for 9 years. Find the sum (principal)?
a)Rs 8000 b)Rs 6000 c)Rs 5000 d)Rs 4000
Answer: D
Explanation: The
difference between the simple interest obtained in the two cases is Rs 1040.
Let the
principal be P .
(P X 9 X
6
100
) - (P X 4 X
7
100
) = 1040
ð $\frac{54P}{100}$
- $\frac{26P}{100}$
= 1040
ð $\frac{26P}{100}$
=
Rs 1040
ð P=Rs 4000
13 In how many years will a sum of money becomes 4 times at 5% p.a
simple interest?
a) 40 years b)50 years c)60 years d)25 years
Answer:C
Explanation:
Sum of money becomes 4 times=> Amount= 4P
Amount= (P+ SI) =>Simple
interest= (4P-P)
SI = P x T x
R
100
=> 3P= P X T X
5
100
ð T=
60 years
14. A sum of money becomes 4 times in 9 years at simple interest. In
how many years will it become 8 times of itself at the same rate?
a)
21 years b)18 years c)15 years d)12 years
Answer:A
Explanation:A
sum of money ( principal) P becomes 4 times => Amount= 4P
Simple interest obtained is 3P
To get simple interest 3P, it takes 9 years.
To get simple interest P, it takes
9
3
= 3 years
Now it has to
become 8 times => The simple interest to be obtained is 7P
To get simple
interest P, it take s 3 years
So to get 7P as simple interest, it takes (7 x 3) = 21 years
15. Mr.Gupta purchased an Apple mobile.He paid 12000 in cash and
promised to pay Rs 40,320 after 3 years. If the rate of interest is 4% p.a,
what is the price of the Mobile at present?
a)Rs 40000 b)Rs 48000 c)Rs
50000 d)Rs 52000
Answer:B
Explanation:
Rs 40,320 to be paid after 3 years is equal to P at present.
Amount = P x
(100+RT)
100
ð 40320=
P x
(100+ 3 X 4)
100
ð P=
40320 x $\frac{100}{112}$
= Rs 36000
Price
of the mobile at present= (Rs 36000+ Rs 12000) = Rs 48000
16. A certain sum of money amounts to Rs 2400 in 3 years and Rs 2720
in 5 years. Find the principal?
a)
Rs 1920 b)Rs 2050 c)Rs 2140 d)Rs
2250
Answer:A
Explanation:
We know that Amount= Principal + Simple Interest
Principal + SI for 5 years= Rs 2720 (i)
Prinipical + SI for 3 years= Rs 2400 --(ii)
(i)-(ii)
gives the SI for 2 years = 320
Simple interest for one year = Rs
320
2
=
160
Given
(P+SI for 3 years)= 2400
ð P
+ (3 x 160) = 2400 =>P=(2400-480) = Rs 1920
17. A sum of money Rs 32000 is lent in two parts, one at the rate of
10% and another at 12% . If the annual interest received is Rs 3600. What is
the amount lent at 12%?
a)Rs 15000 b)Rs 18000 c)Rs
20000 d)Rs 24000
Answer:C
Explanation:
Let P be the money lent at 10% .
Then
(32000- P) is lent at 12%
Simple
interest on both amounts is equal to Rs 3600
P X
1 X
10
100
+ (32000-P) X 1 X
12
100
= 3600
ð $\frac{10P}{100}$
+ 32000X $\frac{12}{100}$ – $\frac{12P}{100}$= 3600
ð $\frac{2P}{100}$
= (3840-3600)
ð 2P=
240 X 100 =>P =Rs 12000
Money lent at 12%= (32000-12000)= 20000.
Money lent at 12%= (32000-12000)= 20000.